$1.$ A five$-$year bond with a yield of $11\%($continuously compounded$)$ pays an $8\%$ coupon at the end of each year.

$($a$)$ What is the bond$$s price?

$($b$)$ What is the bond$$s duration?

$($c$)$ Use the duration to calculate the effect on the bond$$s price of a $0\mathrm{.}2\%$ decrease in its yield.

$($d$)$ Recalculate the bond$$s price on the basis of a $10\mathrm{.}8\%$ per annum yield and verify that the result is in agreement with your answer to $($c$).$

$2.$ The default probability of a company is $5\%$ each year. What is the probability that the company will default in the first three years?